White Privilege does exist, and there is a real, though slight, benefit to being "white," just as there is something of a detriment to being something other than "white" in our society. Old prejudices die hard.
But for better or for worse, there are myriad avenues where non-"whites" can flip that White Privilege on its head. For example, employment in the public sector, in academe, and in many industries actually FAVORS "minorities," especially those who can accumulate appropriate credentials - comparable to what a "white" person would have to have for the position, promotion, award, or what have you. In those areas, Minorities have a BETTER chance of getting that job, promotion, school admission, etc., than a "white" person with comparable credentials.
But ultimately, cultural factors and personal decisions are vastly more important in determining one's chances for success in our society. Consider one fact (according to the U.S. Census Bureau): A "white" child being raised by a single parent is THREE TIMES MORE LIKELY to be raised in poverty than a black child who is raised in an intact family. The white child's "privilege" is nowhere near advantageous enough to overcome his mother's decision (if it was that) to have a child outside marriage.
The wretched state of "minorities" in this country (lower income, less wealth, lower average education attainment, higher unemployment, etc.), is determined to a much greater extent by cultural factors than it is by the vestiges of racism - which cannot be denied or eliminated altogether
Single parenthood, dropping out of school, engaging in criminal activity, declining to pursue and retain opportunities for employment, substance abuse, and on and on and on. Indeed, any American who wants to minimize his chances of living in long-term poverty has to do only three simple things: (1) graduate from high school, (2) don't have children out of wedlock, and (3) get a job - any job, and keep it. Refraining from criminal activity is also nice. Not a high bar, is it?
But minorities have found and are clinging to the phenomenon of "White Privilege" to excuse their profound lack of success, blaming that ethereal, unmeasurable curse rather than the more substantive factors that CAN BE CONTROLLED by good decision-making and personal diligence.